LMFDB - Embedded newform 864.2.y.c.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.6
Character	$\chi$	$=$	864.193
Dual form			864.2.y.c.385.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.523926 - 1.65091i) q^{3} +(-0.649143 + 3.68147i) q^{5} +(-1.60562 + 1.34727i) q^{7} +(-2.45100 - 1.72991i) q^{9} +O(q^{10})$	\(q+(0.523926 - 1.65091i) q^{3} +(-0.649143 + 3.68147i) q^{5} +(-1.60562 + 1.34727i) q^{7} +(-2.45100 - 1.72991i) q^{9} +(-0.730858 - 4.14490i) q^{11} +(-2.93949 + 1.06989i) q^{13} +(5.73767 + 3.00049i) q^{15} +(-0.103757 + 0.179712i) q^{17} +(-1.10111 - 1.90718i) q^{19} +(1.38300 + 3.35660i) q^{21} +(-6.25355 - 5.24735i) q^{23} +(-8.43338 - 3.06950i) q^{25} +(-4.14006 + 3.14004i) q^{27} +(-8.80597 - 3.20511i) q^{29} +(3.28769 + 2.75870i) q^{31} +(-7.22577 - 0.965040i) q^{33} +(-3.91768 - 6.78562i) q^{35} +(2.93827 - 5.08923i) q^{37} +(0.226213 + 5.41337i) q^{39} +(7.94006 - 2.88995i) q^{41} +(0.669113 + 3.79473i) q^{43} +(7.95965 - 7.90034i) q^{45} +(4.35696 - 3.65593i) q^{47} +(-0.452672 + 2.56723i) q^{49} +(0.242328 + 0.265449i) q^{51} -12.5070 q^{53} +15.7338 q^{55} +(-3.72549 + 0.818615i) q^{57} +(-1.72153 + 9.76330i) q^{59} +(-6.65204 + 5.58172i) q^{61} +(6.26604 - 0.524603i) q^{63} +(-2.03061 - 11.5162i) q^{65} +(-1.02697 + 0.373785i) q^{67} +(-11.9393 + 7.57483i) q^{69} +(-2.33322 + 4.04125i) q^{71} +(4.90201 + 8.49053i) q^{73} +(-9.48593 + 12.3146i) q^{75} +(6.75780 + 5.67047i) q^{77} +(2.47506 + 0.900847i) q^{79} +(3.01484 + 8.48002i) q^{81} +(-6.67269 - 2.42866i) q^{83} +(-0.594253 - 0.498637i) q^{85} +(-9.90502 + 12.8586i) q^{87} +(5.28661 + 9.15667i) q^{89} +(3.27827 - 5.67813i) q^{91} +(6.27687 - 3.98233i) q^{93} +(7.73601 - 2.81568i) q^{95} +(-0.431152 - 2.44518i) q^{97} +(-5.37896 + 11.4235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) $ 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.523926	−	1.65091i	0.302489	−	0.953153i
$3$	0.523926	−	1.65091i	0.302489	−	0.953153i
$4$		0			0
$5$	−0.649143	+	3.68147i	−0.290305	+	1.64640i	0.395388	+	0.918514i	$0.370610\pi$
$5$	−0.649143	+	3.68147i	−0.290305	+	1.64640i	−0.685694	+	0.727890i	$0.740501\pi$
$6$		0			0
$7$	−1.60562	+	1.34727i	−0.606867	+	0.509222i	−0.893645	−	0.448775i	$-0.851860\pi$
$7$	−1.60562	+	1.34727i	−0.606867	+	0.509222i	0.286778	+	0.957997i	$0.407416\pi$
$8$		0			0
$9$	−2.45100	−	1.72991i	−0.817001	−	0.576636i
$10$		0			0
$11$	−0.730858	−	4.14490i	−0.220362	−	1.24974i	−0.871356	−	0.490652i	$-0.836759\pi$
$11$	−0.730858	−	4.14490i	−0.220362	−	1.24974i	0.650994	−	0.759083i	$-0.274352\pi$
$12$		0			0
$13$	−2.93949	+	1.06989i	−0.815268	+	0.296733i	−0.715798	−	0.698307i	$-0.753937\pi$
$13$	−2.93949	+	1.06989i	−0.815268	+	0.296733i	−0.0994699	+	0.995041i	$0.531715\pi$
$14$		0			0
$15$	5.73767	+	3.00049i	1.48146	+	0.774724i
$16$		0			0
$17$	−0.103757	+	0.179712i	−0.0251648	+	0.0435866i	−0.878334	−	0.478048i	$-0.841344\pi$
$17$	−0.103757	+	0.179712i	−0.0251648	+	0.0435866i	0.853169	+	0.521635i	$0.174678\pi$
$18$		0			0
$19$	−1.10111	−	1.90718i	−0.252612	−	0.437538i	0.711632	−	0.702553i	$-0.247956\pi$
$19$	−1.10111	−	1.90718i	−0.252612	−	0.437538i	−0.964244	+	0.265015i	$0.914623\pi$
$20$		0			0
$21$	1.38300	+	3.35660i	0.301796	+	0.732471i
$22$		0			0
$23$	−6.25355	−	5.24735i	−1.30396	−	1.09415i	−0.989447	−	0.144894i	$-0.953716\pi$
$23$	−6.25355	−	5.24735i	−1.30396	−	1.09415i	−0.314509	−	0.949255i	$-0.601840\pi$
$24$		0			0
$25$	−8.43338	−	3.06950i	−1.68668	−	0.613900i
$26$		0			0
$27$	−4.14006	+	3.14004i	−0.796756	+	0.604302i
$28$		0			0
$29$	−8.80597	−	3.20511i	−1.63523	−	0.595174i	−0.649032	−	0.760761i	$-0.724826\pi$
$29$	−8.80597	−	3.20511i	−1.63523	−	0.595174i	−0.986195	+	0.165586i	$0.947048\pi$
$30$		0			0
$31$	3.28769	+	2.75870i	0.590487	+	0.495477i	0.888372	−	0.459125i	$-0.151837\pi$
$31$	3.28769	+	2.75870i	0.590487	+	0.495477i	−0.297885	+	0.954602i	$0.596281\pi$
$32$		0			0
$33$	−7.22577	−	0.965040i	−1.25785	−	0.167992i
$34$		0			0
$35$	−3.91768	−	6.78562i	−0.662208	−	1.14698i
$36$		0			0
$37$	2.93827	−	5.08923i	0.483049	−	0.836665i	−0.516762	−	0.856129i	$-0.672863\pi$
$37$	2.93827	−	5.08923i	0.483049	−	0.836665i	0.999811	+	0.0194644i	$0.00619611\pi$
$38$		0			0
$39$	0.226213	+	5.41337i	0.0362230	+	0.866834i
$40$		0			0
$41$	7.94006	−	2.88995i	1.24003	−	0.451334i	0.363008	−	0.931786i	$-0.381750\pi$
$41$	7.94006	−	2.88995i	1.24003	−	0.451334i	0.877021	+	0.480452i	$0.159527\pi$
$42$		0			0
$43$	0.669113	+	3.79473i	0.102039	+	0.578691i	0.992362	+	0.123361i	$0.0393674\pi$
$43$	0.669113	+	3.79473i	0.102039	+	0.578691i	−0.890323	+	0.455329i	$0.849522\pi$
$44$		0			0
$45$	7.95965	−	7.90034i	1.18656	−	1.17771i
$46$		0			0
$47$	4.35696	−	3.65593i	0.635528	−	0.533272i	−0.267113	−	0.963665i	$-0.586070\pi$
$47$	4.35696	−	3.65593i	0.635528	−	0.533272i	0.902641	+	0.430394i	$0.141625\pi$
$48$		0			0
$49$	−0.452672	+	2.56723i	−0.0646675	+	0.366747i
$50$		0			0
$51$	0.242328	+	0.265449i	0.0339327	+	0.0371703i
$52$		0			0
$53$	−12.5070			−1.71797			−0.858983	−	0.512005i	$-0.828903\pi$
$53$	−12.5070			−1.71797			−0.858983	+	0.512005i	$0.828903\pi$
$54$		0			0
$55$	15.7338			2.12154
$56$		0			0
$57$	−3.72549	+	0.818615i	−0.493453	+	0.108428i
$58$		0			0
$59$	−1.72153	+	9.76330i	−0.224125	+	1.27107i	0.640227	+	0.768186i	$0.278840\pi$
$59$	−1.72153	+	9.76330i	−0.224125	+	1.27107i	−0.864352	+	0.502888i	$0.832271\pi$
$60$		0			0
$61$	−6.65204	+	5.58172i	−0.851706	+	0.714666i	−0.960165	−	0.279435i	$-0.909853\pi$
$61$	−6.65204	+	5.58172i	−0.851706	+	0.714666i	0.108459	+	0.994101i	$0.465408\pi$
$62$		0			0
$63$	6.26604	−	0.524603i	0.789447	−	0.0660938i
$64$		0			0
$65$	−2.03061	−	11.5162i	−0.251866	−	1.42840i
$66$		0			0
$67$	−1.02697	+	0.373785i	−0.125464	+	0.0456651i	−0.403989	−	0.914764i	$-0.632377\pi$
$67$	−1.02697	+	0.373785i	−0.125464	+	0.0456651i	0.278525	+	0.960429i	$0.410154\pi$
$68$		0			0
$69$	−11.9393	+	7.57483i	−1.43732	+	0.911902i
$70$		0			0
$71$	−2.33322	+	4.04125i	−0.276902	+	0.479608i	−0.970613	−	0.240645i	$-0.922641\pi$
$71$	−2.33322	+	4.04125i	−0.276902	+	0.479608i	0.693711	+	0.720253i	$0.255974\pi$
$72$		0			0
$73$	4.90201	+	8.49053i	0.573737	+	0.993742i	0.996178	+	0.0873510i	$0.0278402\pi$
$73$	4.90201	+	8.49053i	0.573737	+	0.993742i	−0.422441	+	0.906391i	$0.638826\pi$
$74$		0			0
$75$	−9.48593	+	12.3146i	−1.09534	+	1.42196i
$76$		0			0
$77$	6.75780	+	5.67047i	0.770123	+	0.646210i
$78$		0			0
$79$	2.47506	+	0.900847i	0.278466	+	0.101353i	0.477478	−	0.878644i	$-0.341551\pi$
$79$	2.47506	+	0.900847i	0.278466	+	0.101353i	−0.199012	+	0.979997i	$0.563773\pi$
$80$		0			0
$81$	3.01484	+	8.48002i	0.334982	+	0.942224i
$82$		0			0
$83$	−6.67269	−	2.42866i	−0.732423	−	0.266580i	−0.0512328	−	0.998687i	$-0.516315\pi$
$83$	−6.67269	−	2.42866i	−0.732423	−	0.266580i	−0.681190	+	0.732107i	$0.738537\pi$
$84$		0			0
$85$	−0.594253	−	0.498637i	−0.0644557	−	0.0540848i
$86$		0			0
$87$	−9.90502	+	12.8586i	−1.06193	+	1.37859i
$88$		0			0
$89$	5.28661	+	9.15667i	0.560379	+	0.970606i	0.997463	+	0.0711847i	$0.0226780\pi$
$89$	5.28661	+	9.15667i	0.560379	+	0.970606i	−0.437084	+	0.899421i	$0.643989\pi$
$90$		0			0
$91$	3.27827	−	5.67813i	0.343656	−	0.595230i
$92$		0			0
$93$	6.27687	−	3.98233i	0.650881	−	0.412948i
$94$		0			0
$95$	7.73601	−	2.81568i	0.793698	−	0.288883i
$96$		0			0
$97$	−0.431152	−	2.44518i	−0.0437769	−	0.248271i	0.955064	−	0.296399i	$-0.0957857\pi$
$97$	−0.431152	−	2.44518i	−0.0437769	−	0.248271i	−0.998841	+	0.0481277i	$0.984675\pi$
$98$		0			0
$99$	−5.37896	+	11.4235i	−0.540606	+	1.14810i
$100$		0			0
$101$	−0.949067	+	0.796362i	−0.0944357	+	0.0792410i	−0.688783	−	0.724967i	$-0.741855\pi$
$101$	−0.949067	+	0.796362i	−0.0944357	+	0.0792410i	0.594348	+	0.804208i	$0.297410\pi$
$102$		0			0
$103$	2.74841	−	15.5870i	0.270809	−	1.53583i	−0.481159	−	0.876633i	$-0.659784\pi$
$103$	2.74841	−	15.5870i	0.270809	−	1.53583i	0.751968	−	0.659200i	$-0.229105\pi$
$104$		0			0
$105$	−13.2550	+	2.91257i	−1.29356	+	0.284238i
$106$		0			0
$107$	−3.14345			−0.303889			−0.151944	−	0.988389i	$-0.548553\pi$
$107$	−3.14345			−0.303889			−0.151944	+	0.988389i	$0.548553\pi$
$108$		0			0
$109$	14.8824			1.42547			0.712735	−	0.701433i	$-0.247456\pi$
$109$	14.8824			1.42547			0.712735	+	0.701433i	$0.247456\pi$
$110$		0			0
$111$	−6.86243	−	7.51720i	−0.651353	−	0.713501i
$112$		0			0
$113$	−1.72544	+	9.78548i	−0.162316	+	0.920540i	0.789473	+	0.613786i	$0.210354\pi$
$113$	−1.72544	+	9.78548i	−0.162316	+	0.920540i	−0.951789	+	0.306754i	$0.900757\pi$
$114$		0			0
$115$	23.3774	−	19.6160i	2.17996	−	1.82920i
$116$		0			0
$117$	9.05551	+	2.46275i	0.837182	+	0.227681i
$118$		0			0
$119$	−0.0755277	−	0.428339i	−0.00692361	−	0.0392657i
$120$		0			0
$121$	−6.30944	+	2.29645i	−0.573586	+	0.208768i
$122$		0			0
$123$	−0.611038	−	14.6224i	−0.0550955	−	1.31846i
$124$		0			0
$125$	7.42908	−	12.8675i	0.664477	−	1.15091i
$126$		0			0
$127$	2.44048	+	4.22704i	0.216558	+	0.375089i	0.953753	−	0.300590i	$-0.0971836\pi$
$127$	2.44048	+	4.22704i	0.216558	+	0.375089i	−0.737195	+	0.675680i	$0.763850\pi$
$128$		0			0
$129$	6.61532	+	0.883510i	0.582446	+	0.0777887i
$130$		0			0
$131$	−15.4793	−	12.9887i	−1.35243	−	1.13482i	−0.978241	−	0.207472i	$-0.933476\pi$
$131$	−15.4793	−	12.9887i	−1.35243	−	1.13482i	−0.374190	−	0.927352i	$-0.622079\pi$
$132$		0			0
$133$	4.33746	+	1.57871i	0.376106	+	0.136891i
$134$		0			0
$135$	−8.87249	−	17.2799i	−0.763622	−	1.48721i
$136$		0			0
$137$	−2.02113	−	0.735630i	−0.172677	−	0.0628491i	0.254235	−	0.967142i	$-0.418176\pi$
$137$	−2.02113	−	0.735630i	−0.172677	−	0.0628491i	−0.426912	+	0.904293i	$0.640399\pi$
$138$		0			0
$139$	3.00272	+	2.51959i	0.254688	+	0.213708i	0.761188	−	0.648532i	$-0.224617\pi$
$139$	3.00272	+	2.51959i	0.254688	+	0.213708i	−0.506500	+	0.862240i	$0.669061\pi$
$140$		0			0
$141$	−3.75288	−	9.10839i	−0.316049	−	0.767064i
$142$		0			0
$143$	6.58293	+	11.4020i	0.550492	+	0.953480i
$144$		0			0
$145$	17.5159	−	30.3384i	1.45461	−	2.51946i
$146$		0			0
$147$	4.00110	+	2.09236i	0.330005	+	0.172575i
$148$		0			0
$149$	−8.25256	+	3.00369i	−0.676076	+	0.246072i	−0.657162	−	0.753750i	$-0.728243\pi$
$149$	−8.25256	+	3.00369i	−0.676076	+	0.246072i	−0.0189143	+	0.999821i	$0.506021\pi$
$150$		0			0
$151$	1.02066	+	5.78848i	0.0830605	+	0.471060i	0.997758	+	0.0669210i	$0.0213175\pi$
$151$	1.02066	+	5.78848i	0.0830605	+	0.471060i	−0.914698	+	0.404139i	$0.867571\pi$
$152$		0			0
$153$	0.565194	−	0.260986i	0.0456932	−	0.0210994i
$154$		0			0
$155$	−12.2903	+	10.3127i	−0.987177	+	0.828340i
$156$		0			0
$157$	−0.402343	+	2.28180i	−0.0321104	+	0.182107i	−0.996645	−	0.0818507i	$-0.973917\pi$
$157$	−0.402343	+	2.28180i	−0.0321104	+	0.182107i	0.964534	+	0.263958i	$0.0850281\pi$
$158$		0			0
$159$	−6.55272	+	20.6479i	−0.519665	+	1.63748i
$160$		0			0
$161$	17.1105			1.34849
$162$		0			0
$163$	−15.8520			−1.24162			−0.620810	−	0.783961i	$-0.713196\pi$
$163$	−15.8520			−1.24162			−0.620810	+	0.783961i	$0.713196\pi$
$164$		0			0
$165$	8.24332	−	25.9750i	0.641742	−	2.02215i
$166$		0			0
$167$	1.27375	−	7.22378i	0.0985655	−	0.558993i	−0.895031	−	0.446004i	$-0.852847\pi$
$167$	1.27375	−	7.22378i	0.0985655	−	0.558993i	0.993596	−	0.112988i	$-0.0360423\pi$
$168$		0			0
$169$	−2.46263	+	2.06639i	−0.189433	+	0.158953i
$170$		0			0
$171$	−0.600418	+	6.57933i	−0.0459151	+	0.503134i
$172$		0			0
$173$	−1.54766	−	8.77719i	−0.117666	−	0.667317i	−0.985396	−	0.170281i	$-0.945533\pi$
$173$	−1.54766	−	8.77719i	−0.117666	−	0.667317i	0.867730	−	0.497037i	$-0.165579\pi$
$174$		0			0
$175$	17.6763	−	6.43363i	1.33620	−	0.486337i
$176$		0			0
$177$	15.2164	+	7.95734i	1.14373	+	0.598110i
$178$		0			0
$179$	12.6601	−	21.9279i	0.946261	−	1.63897i	0.193054	−	0.981188i	$-0.438161\pi$
$179$	12.6601	−	21.9279i	0.946261	−	1.63897i	0.753207	−	0.657784i	$-0.228506\pi$
$180$		0			0
$181$	4.01344	+	6.95148i	0.298316	+	0.516699i	0.975751	−	0.218884i	$-0.0702416\pi$
$181$	4.01344	+	6.95148i	0.298316	+	0.516699i	−0.677434	+	0.735583i	$0.736908\pi$
$182$		0			0
$183$	5.72974	+	13.9063i	0.423555	+	1.02798i
$184$		0			0
$185$	16.8285	+	14.1208i	1.23726	+	1.03818i
$186$		0			0
$187$	0.820721	+	0.298718i	0.0600171	+	0.0218444i
$188$		0			0
$189$	2.41687	−	10.6195i	0.175801	−	0.772456i
$190$		0			0
$191$	−10.8320	−	3.94252i	−0.783775	−	0.285271i	−0.0810288	−	0.996712i	$-0.525821\pi$
$191$	−10.8320	−	3.94252i	−0.783775	−	0.285271i	−0.702746	+	0.711441i	$0.748043\pi$
$192$		0			0
$193$	−18.7086	−	15.6984i	−1.34667	−	1.12999i	−0.979857	−	0.199701i	$-0.936003\pi$
$193$	−18.7086	−	15.6984i	−1.34667	−	1.12999i	−0.366818	−	0.930293i	$-0.619553\pi$
$194$		0			0
$195$	−20.0760	−	2.68126i	−1.43767	−	0.192009i
$196$		0			0
$197$	0.299049	+	0.517968i	0.0213063	+	0.0369037i	0.876482	−	0.481435i	$-0.159884\pi$
$197$	0.299049	+	0.517968i	0.0213063	+	0.0369037i	−0.855176	+	0.518338i	$0.826551\pi$
$198$		0			0
$199$	4.19007	−	7.25741i	0.297026	−	0.514464i	−0.678428	−	0.734667i	$-0.737339\pi$
$199$	4.19007	−	7.25741i	0.297026	−	0.514464i	0.975454	+	0.220203i	$0.0706719\pi$
$200$		0			0
$201$	0.0790316	+	1.89126i	0.00557446	+	0.133399i
$202$		0			0
$203$	18.4572	−	6.71787i	1.29544	−	0.471502i
$204$		0			0
$205$	5.48502	+	31.1071i	0.383090	+	2.17261i
$206$		0			0
$207$	6.25005	+	23.6793i	0.434408	+	1.64583i
$208$		0			0
$209$	−7.10033	+	5.95788i	−0.491140	+	0.412115i
$210$		0			0
$211$	−0.927069	+	5.25767i	−0.0638221	+	0.361953i	0.936125	+	0.351667i	$0.114385\pi$
$211$	−0.927069	+	5.25767i	−0.0638221	+	0.361953i	−0.999947	+	0.0102856i	$0.996726\pi$
$212$		0			0
$213$	5.44931	+	5.96925i	0.373380	+	0.409006i
$214$		0			0
$215$	−14.4045			−0.982381
$216$		0			0
$217$	−8.99551			−0.610655
$218$		0			0
$219$	16.5854	−	3.64437i	1.12074	−	0.246264i
$220$		0			0
$221$	0.112721	−	0.639271i	0.00758241	−	0.0430020i
$222$		0			0
$223$	−5.62320	+	4.71842i	−0.376557	+	0.315969i	−0.811349	−	0.584562i	$-0.801266\pi$
$223$	−5.62320	+	4.71842i	−0.376557	+	0.315969i	0.434792	+	0.900531i	$0.356822\pi$
$224$		0			0
$225$	15.3603	+	22.1123i	1.02402	+	1.47415i
$226$		0			0
$227$	−0.927847	−	5.26208i	−0.0615834	−	0.349257i	−0.999993	−	0.00373197i	$-0.998812\pi$
$227$	−0.927847	−	5.26208i	−0.0615834	−	0.349257i	0.938410	−	0.345525i	$-0.112299\pi$
$228$		0			0
$229$	13.3138	−	4.84582i	0.879799	−	0.320221i	0.137671	−	0.990478i	$-0.456038\pi$
$229$	13.3138	−	4.84582i	0.879799	−	0.320221i	0.742129	+	0.670257i	$0.233816\pi$
$230$		0			0
$231$	12.9020	−	8.18562i	0.848890	−	0.538574i
$232$		0			0
$233$	11.2250	−	19.4423i	0.735374	−	1.27371i	−0.219185	−	0.975683i	$-0.570340\pi$
$233$	11.2250	−	19.4423i	0.735374	−	1.27371i	0.954559	−	0.298022i	$-0.0963269\pi$
$234$		0			0
$235$	10.6309	+	18.4133i	0.693483	+	1.20115i
$236$		0			0
$237$	2.78396	−	3.61412i	0.180838	−	0.234762i
$238$		0			0
$239$	−21.2492	−	17.8302i	−1.37450	−	1.15334i	−0.971198	−	0.238272i	$-0.923419\pi$
$239$	−21.2492	−	17.8302i	−1.37450	−	1.15334i	−0.403299	−	0.915068i	$-0.632137\pi$
$240$		0			0
$241$	6.97868	+	2.54003i	0.449536	+	0.163618i	0.556860	−	0.830606i	$-0.312006\pi$
$241$	6.97868	+	2.54003i	0.449536	+	0.163618i	−0.107324	+	0.994224i	$0.534228\pi$
$242$		0			0
$243$	15.5793	−	0.534333i	0.999412	−	0.0342775i
$244$		0			0
$245$	−9.15734	−	3.33300i	−0.585041	−	0.212938i
$246$		0			0
$247$	5.27718	+	4.42808i	0.335779	+	0.281752i
$248$		0			0
$249$	−7.50549	+	9.74357i	−0.475641	+	0.617474i
$250$		0			0
$251$	−9.93026	−	17.1997i	−0.626792	−	1.08564i	−0.988191	−	0.153225i	$-0.951034\pi$
$251$	−9.93026	−	17.1997i	−0.626792	−	1.08564i	0.361399	−	0.932411i	$-0.382299\pi$
$252$		0			0
$253$	−17.1793	+	29.7554i	−1.08005	+	1.87071i
$254$		0			0
$255$	−1.13455	+	0.719808i	−0.0710482	+	0.0450762i
$256$		0			0
$257$	−2.88922	+	1.05159i	−0.180224	+	0.0655963i	−0.430556	−	0.902564i	$-0.641683\pi$
$257$	−2.88922	+	1.05159i	−0.180224	+	0.0655963i	0.250332	+	0.968160i	$0.419460\pi$
$258$		0			0
$259$	2.13885	+	12.1300i	0.132902	+	0.753723i
$260$		0			0
$261$	16.0389	+	23.0893i	0.992785	+	1.42919i
$262$		0			0
$263$	0.567490	−	0.476181i	0.0349929	−	0.0293626i	−0.625123	−	0.780526i	$-0.714951\pi$
$263$	0.567490	−	0.476181i	0.0349929	−	0.0293626i	0.660116	+	0.751163i	$0.270507\pi$
$264$		0			0
$265$	8.11881	−	46.0441i	0.498735	−	2.82846i
$266$		0			0
$267$	17.8866	−	3.93030i	1.09464	−	0.240530i
$268$		0			0
$269$	24.5154			1.49473			0.747365	−	0.664414i	$-0.231319\pi$
$269$	24.5154			1.49473			0.747365	+	0.664414i	$0.231319\pi$
$270$		0			0
$271$	−14.6529			−0.890100			−0.445050	−	0.895506i	$-0.646814\pi$
$271$	−14.6529			−0.890100			−0.445050	+	0.895506i	$0.646814\pi$
$272$		0			0
$273$	−7.65651	−	8.38705i	−0.463393	−	0.507607i
$274$		0			0
$275$	−6.55917	+	37.1989i	−0.395533	+	2.24318i
$276$		0			0
$277$	−10.0694	+	8.44919i	−0.605009	+	0.507663i	−0.893051	−	0.449955i	$-0.851440\pi$
$277$	−10.0694	+	8.44919i	−0.605009	+	0.507663i	0.288042	+	0.957618i	$0.406996\pi$
$278$		0			0
$279$	−3.28585	−	12.4490i	−0.196719	−	0.745301i
$280$		0			0
$281$	4.71855	+	26.7602i	0.281485	+	1.59638i	0.717577	+	0.696479i	$0.245251\pi$
$281$	4.71855	+	26.7602i	0.281485	+	1.59638i	−0.436092	+	0.899902i	$0.643638\pi$
$282$		0			0
$283$	−13.6101	+	4.95367i	−0.809036	+	0.294465i	−0.713226	−	0.700935i	$-0.752766\pi$
$283$	−13.6101	+	4.95367i	−0.809036	+	0.294465i	−0.0958105	+	0.995400i	$0.530544\pi$
$284$		0			0
$285$	−0.595336	−	14.2467i	−0.0352646	−	0.843900i
$286$		0			0
$287$	−8.85517	+	15.3376i	−0.522704	+	0.905350i
$288$		0			0
$289$	8.47847	+	14.6851i	0.498733	+	0.863832i
$290$		0			0
$291$	−4.26267	−	0.569302i	−0.249882	−	0.0333731i
$292$		0			0
$293$	1.77791	+	1.49184i	0.103867	+	0.0871545i	0.693242	−	0.720705i	$-0.256182\pi$
$293$	1.77791	+	1.49184i	0.103867	+	0.0871545i	−0.589375	+	0.807859i	$0.700626\pi$
$294$		0			0
$295$	−34.8258	−	12.6755i	−2.02764	−	0.737999i
$296$		0			0
$297$	16.0410	+	14.8652i	0.930792	+	0.862568i
$298$		0			0
$299$	23.9963	+	8.73395i	1.38774	+	0.505097i
$300$		0			0
$301$	−6.18688	−	5.19141i	−0.356606	−	0.299228i
$302$		0			0
$303$	0.817481	+	1.98406i	0.0469630	+	0.113981i
$304$		0			0
$305$	−16.2308	−	28.1126i	−0.929374	−	1.60972i
$306$		0			0
$307$	−13.2277	+	22.9110i	−0.754943	+	1.30760i	0.190459	+	0.981695i	$0.439002\pi$
$307$	−13.2277	+	22.9110i	−0.754943	+	1.30760i	−0.945402	+	0.325905i	$0.894331\pi$
$308$		0			0
$309$	−24.2928	−	12.7038i	−1.38197	−	0.722694i
$310$		0			0
$311$	31.6994	−	11.5376i	1.79751	−	0.654240i	0.798902	−	0.601461i	$-0.205415\pi$
$311$	31.6994	−	11.5376i	1.79751	−	0.654240i	0.998606	−	0.0527784i	$-0.0168077\pi$
$312$		0			0
$313$	0.831007	+	4.71288i	0.0469713	+	0.266387i	0.999245	−	0.0388589i	$-0.0123723\pi$
$313$	0.831007	+	4.71288i	0.0469713	+	0.266387i	−0.952273	+	0.305246i	$0.901261\pi$
$314$		0			0
$315$	−2.13624	+	23.4088i	−0.120364	+	1.31894i
$316$		0			0
$317$	−16.6351	+	13.9585i	−0.934321	+	0.783989i	−0.976588	−	0.215118i	$-0.930987\pi$
$317$	−16.6351	+	13.9585i	−0.934321	+	0.783989i	0.0422667	+	0.999106i	$0.486542\pi$
$318$		0			0
$319$	−6.84896	+	38.8424i	−0.383468	+	2.17476i
$320$		0			0
$321$	−1.64693	+	5.18955i	−0.0919229	+	0.289653i
$322$		0			0
$323$	0.456992			0.0254277
$324$		0			0
$325$	28.0739			1.55726
$326$		0			0
$327$	7.79724	−	24.5694i	0.431189	−	1.35869i
$328$		0			0
$329$	−2.07009	+	11.7401i	−0.114128	+	0.647250i
$330$		0			0
$331$	20.3631	−	17.0867i	1.11926	−	0.939170i	0.120692	−	0.992690i	$-0.461489\pi$
$331$	20.3631	−	17.0867i	1.11926	−	0.939170i	0.998567	+	0.0535202i	$0.0170442\pi$
$332$		0			0
$333$	−16.0056	+	7.39080i	−0.877102	+	0.405013i
$334$		0			0
$335$	−0.709432	−	4.02339i	−0.0387604	−	0.219821i
$336$		0			0
$337$	6.16270	−	2.24304i	0.335704	−	0.122186i	−0.168668	−	0.985673i	$-0.553946\pi$
$337$	6.16270	−	2.24304i	0.335704	−	0.122186i	0.504371	+	0.863487i	$0.331724\pi$
$338$		0			0
$339$	15.2509	+	7.97541i	0.828317	+	0.433165i
$340$		0			0
$341$	9.03171	−	15.6434i	0.489094	−	0.847136i
$342$		0			0
$343$	−10.0679	−	17.4381i	−0.543616	−	0.941570i
$344$		0			0
$345$	−20.1362	−	48.8713i	−1.08410	−	2.63114i
$346$		0			0
$347$	10.5611	+	8.86181i	0.566949	+	0.475727i	0.880632	−	0.473801i	$-0.157118\pi$
$347$	10.5611	+	8.86181i	0.566949	+	0.475727i	−0.313683	+	0.949528i	$0.601563\pi$
$348$		0			0
$349$	9.45672	+	3.44196i	0.506207	+	0.184244i	0.582483	−	0.812843i	$-0.302081\pi$
$349$	9.45672	+	3.44196i	0.506207	+	0.184244i	−0.0762769	+	0.997087i	$0.524303\pi$
$350$		0			0
$351$	8.81019	−	13.6595i	0.470253	−	0.729092i
$352$		0			0
$353$	−16.4124	−	5.97364i	−0.873546	−	0.317945i	−0.133944	−	0.990989i	$-0.542764\pi$
$353$	−16.4124	−	5.97364i	−0.873546	−	0.317945i	−0.739602	+	0.673044i	$0.764986\pi$
$354$		0			0
$355$	−13.3632	−	11.2130i	−0.709243	−	0.595125i
$356$		0			0
$357$	−0.746719	−	0.0997282i	−0.0395206	−	0.00527818i
$358$		0			0
$359$	−9.67705	−	16.7611i	−0.510735	−	0.884620i	−0.999923	−	0.0124408i	$-0.996040\pi$
$359$	−9.67705	−	16.7611i	−0.510735	−	0.884620i	0.489187	−	0.872179i	$-0.337293\pi$
$360$		0			0
$361$	7.07511	−	12.2544i	0.372374	−	0.644971i
$362$		0			0
$363$	0.485552	+	11.6195i	0.0254849	+	0.609865i
$364$		0			0
$365$	−34.4398	+	12.5350i	−1.80266	+	0.656114i
$366$		0			0
$367$	0.885304	+	5.02081i	0.0462125	+	0.262084i	0.999157	−	0.0410619i	$-0.0130741\pi$
$367$	0.885304	+	5.02081i	0.0462125	+	0.262084i	−0.952944	+	0.303146i	$0.901963\pi$
$368$		0			0
$369$	−24.4605	−	6.65230i	−1.27336	−	0.346305i
$370$		0			0
$371$	20.0814	−	16.8503i	1.04258	−	0.874826i
$372$		0			0
$373$	4.13884	−	23.4725i	0.214301	−	1.21536i	−0.667814	−	0.744328i	$-0.732770\pi$
$373$	4.13884	−	23.4725i	0.214301	−	1.21536i	0.882115	−	0.471033i	$-0.156119\pi$
$374$		0			0
$375$	−17.3509	−	19.0064i	−0.895995	−	0.981485i
$376$		0			0
$377$	29.3142			1.50976
$378$		0			0
$379$	32.2796			1.65809			0.829047	−	0.559179i	$-0.188883\pi$
$379$	32.2796			1.65809			0.829047	+	0.559179i	$0.188883\pi$
$380$		0			0
$381$	8.25710	−	1.81436i	0.423024	−	0.0929527i
$382$		0			0
$383$	−3.43768	+	19.4960i	−0.175657	+	0.996201i	0.761726	+	0.647900i	$0.224352\pi$
$383$	−3.43768	+	19.4960i	−0.175657	+	0.996201i	−0.937383	+	0.348301i	$0.886759\pi$
$384$		0			0
$385$	−25.2625	+	21.1977i	−1.28749	+	1.08034i
$386$		0			0
$387$	4.92453	−	10.4584i	0.250328	−	0.531630i
$388$		0			0
$389$	−0.0339823	−	0.192723i	−0.00172297	−	0.00977145i	0.983934	−	0.178532i	$-0.0571347\pi$
$389$	−0.0339823	−	0.192723i	−0.00172297	−	0.00977145i	−0.985657	+	0.168760i	$0.946024\pi$
$390$		0			0
$391$	1.59186	−	0.579391i	0.0805040	−	0.0293011i
$392$		0			0
$393$	−29.5531	+	18.7498i	−1.49076	+	0.945802i
$394$		0			0
$395$	−4.92311	+	8.52707i	−0.247708	+	0.429044i
$396$		0			0
$397$	−4.03231	−	6.98417i	−0.202376	−	0.350525i	0.746918	−	0.664917i	$-0.231533\pi$
$397$	−4.03231	−	6.98417i	−0.202376	−	0.350525i	−0.949293	+	0.314391i	$0.898200\pi$
$398$		0			0
$399$	4.87881	−	6.33364i	0.244246	−	0.317078i
$400$		0			0
$401$	−10.8538	−	9.10742i	−0.542013	−	0.454803i	0.330213	−	0.943906i	$-0.392879\pi$
$401$	−10.8538	−	9.10742i	−0.542013	−	0.454803i	−0.872226	+	0.489104i	$0.837324\pi$
$402$		0			0
$403$	−12.6156	−	4.59172i	−0.628430	−	0.228730i
$404$		0			0
$405$	−33.1760	+	5.59431i	−1.64853	+	0.277984i
$406$		0			0
$407$	−23.2418	−	8.45933i	−1.15205	−	0.419314i
$408$		0			0
$409$	−19.6646	−	16.5005i	−0.972350	−	0.815898i	0.0105681	−	0.999944i	$-0.496636\pi$
$409$	−19.6646	−	16.5005i	−0.972350	−	0.815898i	−0.982918	+	0.184046i	$0.941080\pi$
$410$		0			0
$411$	−2.27338	+	2.95128i	−0.112138	+	0.145576i
$412$		0			0
$413$	−10.3897	−	17.9955i	−0.511245	−	0.885502i
$414$		0			0
$415$	13.2726	−	22.9888i	0.651525	−	1.12847i
$416$		0			0
$417$	5.73281	−	3.63715i	0.280737	−	0.178112i
$418$		0			0
$419$	−27.8084	+	10.1214i	−1.35853	+	0.494465i	−0.915600	−	0.402091i	$-0.868284\pi$
$419$	−27.8084	+	10.1214i	−1.35853	+	0.494465i	−0.442931	+	0.896556i	$0.646061\pi$
$420$		0			0
$421$	0.378014	+	2.14382i	0.0184233	+	0.104484i	0.992633	−	0.121162i	$-0.0386620\pi$
$421$	0.378014	+	2.14382i	0.0184233	+	0.104484i	−0.974209	+	0.225645i	$0.927551\pi$
$422$		0			0
$423$	−17.0033	+	1.42355i	−0.826731	+	0.0692153i
$424$		0			0
$425$	1.42665	−	1.19710i	0.0692026	−	0.0580679i
$426$		0			0
$427$	3.16053	−	17.9242i	0.152949	−	0.867415i
$428$		0			0
$429$	22.2726	−	4.89404i	1.07533	−	0.236286i
$430$		0			0
$431$	34.3474			1.65446			0.827229	−	0.561865i	$-0.189916\pi$
$431$	34.3474			1.65446			0.827229	+	0.561865i	$0.189916\pi$
$432$		0			0
$433$	−29.5843			−1.42173			−0.710864	−	0.703329i	$-0.751696\pi$
$433$	−29.5843			−1.42173			−0.710864	+	0.703329i	$0.751696\pi$
$434$		0			0
$435$	−40.9089	−	44.8121i	−1.96143	−	2.14858i
$436$		0			0
$437$	−3.12180	+	17.7046i	−0.149336	+	0.846925i
$438$		0			0
$439$	−14.8456	+	12.4570i	−0.708544	+	0.594539i	−0.924190	−	0.381933i	$-0.875259\pi$
$439$	−14.8456	+	12.4570i	−0.708544	+	0.594539i	0.215646	+	0.976472i	$0.430814\pi$
$440$		0			0
$441$	5.55058	−	5.50922i	0.264313	−	0.262344i
$442$		0			0
$443$	5.40196	+	30.6360i	0.256655	+	1.45556i	0.791789	+	0.610795i	$0.209150\pi$
$443$	5.40196	+	30.6360i	0.256655	+	1.45556i	−0.535134	+	0.844767i	$0.679739\pi$
$444$		0			0
$445$	−37.1418	+	13.5185i	−1.76069	+	0.640839i
$446$		0			0
$447$	0.635087	+	15.1979i	0.0300386	+	0.718838i
$448$		0			0
$449$	7.72305	−	13.3767i	0.364473	−	0.631286i	−0.624218	−	0.781250i	$-0.714582\pi$
$449$	7.72305	−	13.3767i	0.364473	−	0.631286i	0.988691	+	0.149964i	$0.0479157\pi$
$450$		0			0
$451$	−17.7816	−	30.7986i	−0.837303	−	1.45025i
$452$		0			0
$453$	10.0910	+	1.34771i	0.474117	+	0.0633207i
$454$		0			0
$455$	18.7758	+	15.7548i	0.880224	+	0.738596i
$456$		0			0
$457$	17.5306	+	6.38060i	0.820045	+	0.298472i	0.717766	−	0.696284i	$-0.245165\pi$
$457$	17.5306	+	6.38060i	0.820045	+	0.298472i	0.102278	+	0.994756i	$0.467387\pi$
$458$		0			0
$459$	−0.134744	−	1.06982i	−0.00628931	−	0.0499350i
$460$		0			0
$461$	−23.2643	−	8.46750i	−1.08353	−	0.394371i	−0.262306	−	0.964985i	$-0.584483\pi$
$461$	−23.2643	−	8.46750i	−1.08353	−	0.394371i	−0.821219	+	0.570614i	$0.806705\pi$
$462$		0			0
$463$	0.00265004	+	0.00222365i	0.000123158	+	0.000103342i	0.642849	−	0.765993i	$-0.277752\pi$
$463$	0.00265004	+	0.00222365i	0.000123158	+	0.000103342i	−0.642726	+	0.766096i	$0.722197\pi$
$464$		0			0
$465$	10.5862	+	25.6932i	0.490925	+	1.19149i
$466$		0			0
$467$	11.7146	+	20.2904i	0.542089	+	0.938926i	0.998784	+	0.0493022i	$0.0156998\pi$
$467$	11.7146	+	20.2904i	0.542089	+	0.938926i	−0.456695	+	0.889623i	$0.650967\pi$
$468$		0			0
$469$	1.14533	−	1.98376i	0.0528862	−	0.0916016i
$470$		0			0
$471$	3.55625	+	1.85972i	0.163863	+	0.0856916i
$472$		0			0
$473$	15.2398	−	5.54682i	0.700725	−	0.255043i
$474$		0			0
$475$	3.43200	+	19.4639i	0.157471	+	0.893063i
$476$		0			0
$477$	30.6547	+	21.6359i	1.40358	+	0.990640i
$478$		0			0
$479$	−10.8123	+	9.07264i	−0.494029	+	0.414539i	−0.855467	−	0.517857i	$-0.826730\pi$
$479$	−10.8123	+	9.07264i	−0.494029	+	0.414539i	0.361439	+	0.932396i	$0.382286\pi$
$480$		0			0
$481$	−3.19211	+	18.1034i	−0.145548	+	0.825443i
$482$		0			0
$483$	8.96460	−	28.2478i	0.407904	−	1.28532i
$484$		0			0
$485$	9.28176			0.421463
$486$		0			0
$487$	−17.3282			−0.785215			−0.392607	−	0.919706i	$-0.628427\pi$
$487$	−17.3282			−0.785215			−0.392607	+	0.919706i	$0.628427\pi$
$488$		0			0
$489$	−8.30524	+	26.1701i	−0.375576	+	1.18345i
$490$		0			0
$491$	3.43165	−	19.4618i	0.154868	−	0.878300i	−0.804038	−	0.594578i	$-0.797319\pi$
$491$	3.43165	−	19.4618i	0.154868	−	0.878300i	0.958906	−	0.283723i	$-0.0915696\pi$
$492$		0			0
$493$	1.48968	−	1.24999i	0.0670917	−	0.0562967i
$494$		0			0
$495$	−38.5635	−	27.2180i	−1.73330	−	1.22336i
$496$		0			0
$497$	−1.69842	−	9.63220i	−0.0761844	−	0.432063i
$498$		0			0
$499$	18.1534	−	6.60731i	0.812659	−	0.295784i	0.0979374	−	0.995193i	$-0.468776\pi$
$499$	18.1534	−	6.60731i	0.812659	−	0.295784i	0.714722	+	0.699409i	$0.246553\pi$
$500$		0			0
$501$	−11.2585	−	5.88756i	−0.502991	−	0.263037i
$502$		0			0
$503$	−3.52469	+	6.10495i	−0.157158	+	0.272206i	−0.933843	−	0.357684i	$-0.883567\pi$
$503$	−3.52469	+	6.10495i	−0.157158	+	0.272206i	0.776685	+	0.629890i	$0.216900\pi$
$504$		0			0
$505$	−2.31570	−	4.01092i	−0.103047	−	0.178483i
$506$		0			0
$507$	2.12119	+	5.14821i	0.0942054	+	0.228640i
$508$		0			0
$509$	−4.92044	−	4.12874i	−0.218095	−	0.183003i	0.527194	−	0.849745i	$-0.323244\pi$
$509$	−4.92044	−	4.12874i	−0.218095	−	0.183003i	−0.745289	+	0.666742i	$0.767688\pi$
$510$		0			0
$511$	−19.3098	−	7.02821i	−0.854217	−	0.310910i
$512$		0			0
$513$	10.5473	+	4.43832i	0.465675	+	0.195956i
$514$		0			0
$515$	55.5990	+	20.2364i	2.44998	+	0.891721i
$516$		0			0
$517$	−18.3378	−	15.3872i	−0.806495	−	0.676729i
$518$		0			0
$519$	−15.3012	−	2.04355i	−0.671648	−	0.0897021i
$520$		0			0
$521$	4.50107	+	7.79608i	0.197196	+	0.341553i	0.947618	−	0.319406i	$-0.103483\pi$
$521$	4.50107	+	7.79608i	0.197196	+	0.341553i	−0.750423	+	0.660958i	$0.770150\pi$
$522$		0			0
$523$	−13.5968	+	23.5503i	−0.594546	+	1.02978i	0.399064	+	0.916923i	$0.369335\pi$
$523$	−13.5968	+	23.5503i	−0.594546	+	1.02978i	−0.993611	+	0.112862i	$0.963998\pi$
$524$		0			0
$525$	−1.36030	−	32.5527i	−0.0593684	−	1.42071i
$526$		0			0
$527$	−0.836893	+	0.304604i	−0.0364556	+	0.0132688i
$528$		0			0
$529$	7.57829	+	42.9786i	0.329491	+	1.86864i
$530$		0			0
$531$	21.1091	−	20.9518i	0.916056	−	0.909230i
$532$		0			0
$533$	−20.2478	+	16.9899i	−0.877030	+	0.735916i
$534$		0			0
$535$	2.04055	−	11.5725i	0.0882206	−	0.500324i
$536$		0			0
$537$	−29.5681	−	32.3893i	−1.27596	−	1.39770i
$538$		0			0
$539$	10.9718			0.472587
$540$		0			0
$541$	25.0285			1.07606			0.538030	−	0.842926i	$-0.319169\pi$
$541$	25.0285			1.07606			0.538030	+	0.842926i	$0.319169\pi$
$542$		0			0
$543$	13.5790	−	2.98376i	0.582731	−	0.128046i
$544$		0			0
$545$	−9.66077	+	54.7889i	−0.413822	+	2.34690i
$546$		0			0
$547$	8.33060	−	6.99020i	0.356191	−	0.298880i	−0.447080	−	0.894494i	$-0.647536\pi$
$547$	8.33060	−	6.99020i	0.356191	−	0.298880i	0.803270	+	0.595615i	$0.203091\pi$
$548$		0			0
$549$	25.9600	−	2.17342i	1.10795	−	0.0927591i
$550$		0			0
$551$	3.58363	+	20.3238i	0.152668	+	0.865822i
$552$		0			0
$553$	−5.18769	+	1.88816i	−0.220603	+	0.0802929i
$554$		0			0
$555$	32.1290	−	20.3841i	1.36380	−	0.865257i
$556$		0			0
$557$	−18.1237	+	31.3911i	−0.767925	+	1.33008i	0.170761	+	0.985312i	$0.445377\pi$
$557$	−18.1237	+	31.3911i	−0.767925	+	1.33008i	−0.938686	+	0.344772i	$0.887956\pi$
$558$		0			0
$559$	−6.02678	−	10.4387i	−0.254906	−	0.441510i
$560$		0			0
$561$	0.923154	−	1.19843i	0.0389756	−	0.0505978i
$562$		0			0
$563$	3.87845	+	3.25441i	0.163457	+	0.137157i	0.720848	−	0.693094i	$-0.243753\pi$
$563$	3.87845	+	3.25441i	0.163457	+	0.137157i	−0.557390	+	0.830251i	$0.688197\pi$
$564$		0			0
$565$	−34.9049	−	12.7043i	−1.46846	−	0.534476i
$566$		0			0
$567$	−16.2656	−	9.55386i	−0.683091	−	0.401225i
$568$		0			0
$569$	3.88765	+	1.41499i	0.162979	+	0.0593194i	0.422221	−	0.906493i	$-0.361251\pi$
$569$	3.88765	+	1.41499i	0.162979	+	0.0593194i	−0.259242	+	0.965812i	$0.583473\pi$
$570$		0			0
$571$	−30.0150	−	25.1855i	−1.25609	−	1.05398i	−0.996087	−	0.0883734i	$-0.971833\pi$
$571$	−30.0150	−	25.1855i	−1.25609	−	1.05398i	−0.260000	−	0.965609i	$-0.583722\pi$
$572$		0			0
$573$	−12.1839	+	15.8170i	−0.508989	+	0.660766i
$574$		0			0
$575$	36.6318	+	63.4482i	1.52765	+	2.64597i
$576$		0			0
$577$	−5.93375	+	10.2775i	−0.247025	+	0.427860i	−0.962699	−	0.270575i	$-0.912786\pi$
$577$	−5.93375	+	10.2775i	−0.247025	+	0.427860i	0.715674	+	0.698435i	$0.246120\pi$
$578$		0			0
$579$	−35.7185	+	22.6614i	−1.48441	+	0.941777i
$580$		0			0
$581$	13.9859	−	5.09044i	0.580232	−	0.211187i
$582$		0			0
$583$	9.14083	+	51.8402i	0.378574	+	2.14700i
$584$		0			0
$585$	−14.9449	+	31.7389i	−0.617894	+	1.31224i
$586$		0			0
$587$	−1.42585	+	1.19643i	−0.0588510	+	0.0493819i	−0.671739	−	0.740788i	$-0.734452\pi$
$587$	−1.42585	+	1.19643i	−0.0588510	+	0.0493819i	0.612888	+	0.790170i	$0.290008\pi$
$588$		0			0
$589$	1.64123	−	9.30786i	0.0676256	−	0.383524i
$590$		0			0
$591$	1.01180	−	0.222326i	0.0416198	−	0.00914527i
$592$		0			0
$593$	−2.04591			−0.0840153			−0.0420076	−	0.999117i	$-0.513375\pi$
$593$	−2.04591			−0.0840153			−0.0420076	+	0.999117i	$0.513375\pi$
$594$		0			0
$595$	1.62594			0.0666572
$596$		0			0
$597$	−9.78604	−	10.7198i	−0.400516	−	0.438731i
$598$		0			0
$599$	1.05689	−	5.99394i	0.0431835	−	0.244906i	−0.955573	−	0.294754i	$-0.904762\pi$
$599$	1.05689	−	5.99394i	0.0431835	−	0.244906i	0.998757	+	0.0498476i	$0.0158736\pi$
$600$		0			0
$601$	5.23948	−	4.39645i	0.213723	−	0.179335i	−0.529641	−	0.848222i	$-0.677673\pi$
$601$	5.23948	−	4.39645i	0.213723	−	0.179335i	0.743364	+	0.668887i	$0.233229\pi$
$602$		0			0
$603$	3.16371	+	0.860407i	0.128836	+	0.0350385i
$604$		0			0
$605$	−4.35858	−	24.7188i	−0.177202	−	1.00496i
$606$		0			0
$607$	−34.9907	+	12.7356i	−1.42023	+	0.516921i	−0.934114	−	0.356975i	$-0.883808\pi$
$607$	−34.9907	+	12.7356i	−1.42023	+	0.516921i	−0.486114	+	0.873895i	$0.661586\pi$
$608$		0			0
$609$	−1.42040	−	33.9908i	−0.0575575	−	1.37738i
$610$		0			0
$611$	−8.89583	+	15.4080i	−0.359887	+	0.623342i
$612$		0			0
$613$	−16.8192	−	29.1317i	−0.679322	−	1.17662i	−0.975185	−	0.221390i	$-0.928941\pi$
$613$	−16.8192	−	29.1317i	−0.679322	−	1.17662i	0.295864	−	0.955230i	$-0.404393\pi$
$614$		0			0
$615$	54.2287	+	7.24253i	2.18671	+	0.292047i
$616$		0			0
$617$	−16.0106	−	13.4345i	−0.644562	−	0.540852i	0.260853	−	0.965378i	$-0.415996\pi$
$617$	−16.0106	−	13.4345i	−0.644562	−	0.540852i	−0.905415	+	0.424527i	$0.860440\pi$
$618$		0			0
$619$	−45.1776	−	16.4433i	−1.81584	−	0.660912i	−0.996105	−	0.0881705i	$-0.971898\pi$
$619$	−45.1776	−	16.4433i	−1.81584	−	0.660912i	−0.819736	−	0.572742i	$-0.805880\pi$
$620$		0			0
$621$	42.3670	+	2.08795i	1.70013	+	0.0837866i
$622$		0			0
$623$	−20.8248	−	7.57962i	−0.834330	−	0.303671i
$624$		0			0
$625$	8.17420	+	6.85897i	0.326968	+	0.274359i
$626$		0			0
$627$	6.11588	+	14.8435i	0.244245	+	0.592792i
$628$		0			0
$629$	0.609732	+	1.05609i	0.0243116	+	0.0421089i
$630$		0			0
$631$	−6.77646	+	11.7372i	−0.269766	+	0.467249i	−0.968801	−	0.247838i	$-0.920280\pi$
$631$	−6.77646	+	11.7372i	−0.269766	+	0.467249i	0.699035	+	0.715088i	$0.253613\pi$
$632$		0			0
$633$	8.19422	+	4.28513i	0.325691	+	0.170319i
$634$		0			0
$635$	−17.1460	+	6.24062i	−0.680417	+	0.247651i
$636$		0			0
$637$	−1.41602	−	8.03066i	−0.0561049	−	0.318187i
$638$		0			0
$639$	12.7097	−	5.86887i	0.502789	−	0.232169i
$640$		0			0
$641$	14.6859	−	12.3230i	0.580060	−	0.486728i	−0.304907	−	0.952382i	$-0.598625\pi$
$641$	14.6859	−	12.3230i	0.580060	−	0.486728i	0.884967	+	0.465654i	$0.154181\pi$
$642$		0			0
$643$	−0.633985	+	3.59551i	−0.0250019	+	0.141793i	−0.994753	−	0.102301i	$-0.967379\pi$
$643$	−0.633985	+	3.59551i	−0.0250019	+	0.141793i	0.969752	+	0.244094i	$0.0784906\pi$
$644$		0			0
$645$	−7.54690	+	23.7806i	−0.297159	+	0.936359i
$646$		0			0
$647$	6.15355			0.241921			0.120960	−	0.992657i	$-0.461403\pi$
$647$	6.15355			0.241921			0.120960	+	0.992657i	$0.461403\pi$
$648$		0			0
$649$	41.7261			1.63789
$650$		0			0
$651$	−4.71298	+	14.8508i	−0.184716	+	0.582048i
$652$		0			0
$653$	7.01971	−	39.8108i	0.274702	−	1.55792i	−0.465203	−	0.885204i	$-0.654019\pi$
$653$	7.01971	−	39.8108i	0.274702	−	1.55792i	0.739905	−	0.672711i	$-0.234870\pi$
$654$		0			0
$655$	57.8656	−	48.5550i	2.26100	−	1.89720i
$656$		0			0
$657$	2.67298	−	29.2904i	0.104283	−	1.14273i
$658$		0			0
$659$	−4.81938	−	27.3321i	−0.187736	−	1.06471i	−0.922389	−	0.386262i	$-0.873766\pi$
$659$	−4.81938	−	27.3321i	−0.187736	−	1.06471i	0.734653	−	0.678443i	$-0.237345\pi$
$660$		0			0
$661$	27.9949	−	10.1893i	1.08887	−	0.396318i	0.265670	−	0.964064i	$-0.414407\pi$
$661$	27.9949	−	10.1893i	1.08887	−	0.396318i	0.823204	+	0.567746i	$0.192184\pi$
$662$		0			0
$663$	−0.996321	−	0.521022i	−0.0386939	−	0.0202348i
$664$		0			0
$665$	−8.62760	+	14.9434i	−0.334564	+	0.579482i
$666$		0			0
$667$	38.2502	+	66.2514i	1.48106	+	2.56526i
$668$		0			0
$669$	4.84355	+	11.7555i	0.187263	+	0.454494i
$670$		0			0
$671$	27.9974	+	23.4926i	1.08083	+	0.906922i
$672$		0			0
$673$	−35.5790	−	12.9497i	−1.37147	−	0.499174i	−0.451888	−	0.892075i	$-0.649249\pi$
$673$	−35.5790	−	12.9497i	−1.37147	−	0.499174i	−0.919581	+	0.392901i	$0.871472\pi$
$674$		0			0
$675$	44.5531	−	13.7733i	1.71485	−	0.530133i
$676$		0			0
$677$	15.3651	+	5.59246i	0.590531	+	0.214936i	0.619963	−	0.784631i	$-0.287148\pi$
$677$	15.3651	+	5.59246i	0.590531	+	0.214936i	−0.0294321	+	0.999567i	$0.509370\pi$
$678$		0			0
$679$	3.98660	+	3.34516i	0.152992	+	0.128375i
$680$		0			0
$681$	−9.17334	−	1.22515i	−0.351523	−	0.0469478i
$682$		0			0
$683$	−0.925722	−	1.60340i	−0.0354218	−	0.0613523i	0.847771	−	0.530362i	$-0.177944\pi$
$683$	−0.925722	−	1.60340i	−0.0354218	−	0.0613523i	−0.883193	+	0.469010i	$0.844611\pi$
$684$		0			0
$685$	4.02020	−	6.96319i	0.153604	−	0.266050i
$686$		0			0
$687$	−1.02458	−	24.5187i	−0.0390902	−	0.935447i
$688$		0			0
$689$	36.7641	−	13.3811i	1.40060	−	0.509778i
$690$		0			0
$691$	5.20961	+	29.5452i	0.198183	+	1.12395i	0.907812	+	0.419376i	$0.137751\pi$
$691$	5.20961	+	29.5452i	0.198183	+	1.12395i	−0.709629	+	0.704575i	$0.751138\pi$
$692$		0			0
$693$	−6.75402	−	25.5887i	−0.256564	−	0.972035i
$694$		0			0
$695$	−11.2250	+	9.41887i	−0.425788	+	0.357278i
$696$		0			0
$697$	−0.304478	+	1.72678i	−0.0115329	+	0.0654064i
$698$		0			0
$699$	−26.2164	−	28.7178i	−0.991594	−	1.08621i
$700$		0			0
$701$	−4.36364			−0.164812			−0.0824062	−	0.996599i	$-0.526260\pi$
$701$	−4.36364			−0.164812			−0.0824062	+	0.996599i	$0.526260\pi$
$702$		0			0
$703$	−12.9415			−0.488096
$704$		0			0
$705$	35.9684	−	7.90348i	1.35465	−	0.297662i
$706$		0			0
$707$	0.450922	−	2.55731i	0.0169587	−	0.0961775i
$708$		0			0
$709$	7.43942	−	6.24241i	0.279393	−	0.234439i	−0.492312	−	0.870419i	$-0.663848\pi$
$709$	7.43942	−	6.24241i	0.279393	−	0.234439i	0.771706	+	0.635980i	$0.219404\pi$
$710$		0			0
$711$	−4.50799	−	6.48960i	−0.169063	−	0.243379i
$712$		0			0
$713$	−6.08387	−	34.5034i	−0.227843	−	1.29216i
$714$		0			0
$715$	−46.2493	+	16.8334i	−1.72962	+	0.629532i
$716$		0			0
$717$	−40.5691	+	25.7388i	−1.51508	+	0.961234i
$718$		0			0
$719$	15.2926	−	26.4875i	0.570317	−	0.987818i	−0.426216	−	0.904621i	$-0.640154\pi$
$719$	15.2926	−	26.4875i	0.570317	−	0.987818i	0.996533	−	0.0831969i	$-0.0265130\pi$
$720$		0			0
$721$	16.5871	+	28.7297i	0.617735	+	1.06995i
$722$		0			0
$723$	7.84967	−	10.1904i	0.291932	−	0.378984i
$724$		0			0
$725$	64.4260	+	54.0598i	2.39272	+	2.00773i
$726$		0			0
$727$	−25.9002	−	9.42690i	−0.960585	−	0.349624i	−0.186322	−	0.982489i	$-0.559657\pi$
$727$	−25.9002	−	9.42690i	−0.960585	−	0.349624i	−0.774263	+	0.632864i	$0.781879\pi$
$728$		0			0
$729$	7.28026	−	26.0000i	0.269639	−	0.962961i
$730$		0			0
$731$	−0.751384	−	0.273482i	−0.0277910	−	0.0101151i
$732$		0			0
$733$	10.3709	+	8.70218i	0.383056	+	0.321422i	0.813901	−	0.581004i	$-0.197340\pi$
$733$	10.3709	+	8.70218i	0.383056	+	0.321422i	−0.430845	+	0.902426i	$0.641784\pi$
$734$		0			0
$735$	−10.3002	+	13.3717i	−0.379930	+	0.493223i
$736$		0			0
$737$	2.29987	+	3.98349i	0.0847168	+	0.146734i
$738$		0			0
$739$	−9.47441	+	16.4102i	−0.348522	+	0.603658i	−0.985987	−	0.166822i	$-0.946650\pi$
$739$	−9.47441	+	16.4102i	−0.348522	+	0.603658i	0.637465	+	0.770479i	$0.279983\pi$
$740$		0			0
$741$	10.0752	−	6.39216i	0.370122	−	0.234822i
$742$		0			0
$743$	2.83261	−	1.03099i	0.103918	−	0.0378232i	−0.289538	−	0.957167i	$-0.593502\pi$
$743$	2.83261	−	1.03099i	0.103918	−	0.0378232i	0.393456	+	0.919343i	$0.371279\pi$
$744$		0			0
$745$	−5.70090	−	32.3314i	−0.208865	−	1.18453i
$746$		0			0
$747$	12.1534	+	17.4958i	0.444671	+	0.640138i
$748$		0			0
$749$	5.04719	−	4.23509i	0.184420	−	0.154747i
$750$		0			0
$751$	−5.21650	+	29.5842i	−0.190353	+	1.07954i	0.728530	+	0.685013i	$0.240204\pi$
$751$	−5.21650	+	29.5842i	−0.190353	+	1.07954i	−0.918883	+	0.394530i	$0.870907\pi$
$752$		0			0
$753$	−33.5979	+	7.38259i	−1.22437	+	0.269036i
$754$		0			0
$755$	−21.9727			−0.799667
$756$		0			0
$757$	43.0207			1.56362			0.781808	−	0.623520i	$-0.214298\pi$
$757$	43.0207			1.56362			0.781808	+	0.623520i	$0.214298\pi$
$758$		0			0
$759$	40.1229	+	43.9511i	1.45637	+	1.59532i
$760$		0			0
$761$	−1.11138	+	6.30293i	−0.0402874	+	0.228481i	−0.998303	−	0.0582352i	$-0.981453\pi$
$761$	−1.11138	+	6.30293i	−0.0402874	+	0.228481i	0.958015	+	0.286716i	$0.0925638\pi$
$762$		0			0
$763$	−23.8954	+	20.0506i	−0.865071	+	0.725881i
$764$		0			0
$765$	0.593920	+	2.25016i	0.0214732	+	0.0813548i
$766$		0			0
$767$	−5.38520	−	30.5410i	−0.194448	−	1.10277i
$768$		0			0
$769$	1.41632	−	0.515497i	0.0510737	−	0.0185893i	−0.316357	−	0.948640i	$-0.602460\pi$
$769$	1.41632	−	0.515497i	0.0510737	−	0.0185893i	0.367431	+	0.930051i	$0.380238\pi$
$770$		0			0
$771$	0.222344	+	5.32079i	0.00800751	+	0.191624i
$772$		0			0
$773$	2.61227	−	4.52459i	0.0939570	−	0.162738i	−0.815216	−	0.579157i	$-0.803382\pi$
$773$	2.61227	−	4.52459i	0.0939570	−	0.162738i	0.909173	+	0.416419i	$0.136715\pi$
$774$		0			0
$775$	−19.2585	−	33.3567i	−0.691786	−	1.19821i
$776$		0			0
$777$	21.1462	+	2.82418i	0.758615	+	0.101317i
$778$		0			0
$779$	−14.2545	−	11.9610i	−0.510722	−	0.428547i
$780$		0			0
$781$	18.4558	+	6.71738i	0.660402	+	0.240367i
$782$		0			0
$783$	46.5215	−	14.3818i	1.66254	−	0.513962i
$784$		0			0
$785$	−8.13920	−	2.96243i	−0.290500	−	0.105734i
$786$		0			0
$787$	−26.6241	−	22.3402i	−0.949045	−	0.796343i	0.0300913	−	0.999547i	$-0.490420\pi$
$787$	−26.6241	−	22.3402i	−0.949045	−	0.796343i	−0.979136	+	0.203204i	$0.934865\pi$
$788$		0			0
$789$	−0.488809	−	1.18636i	−0.0174021	−	0.0422355i
$790$		0			0
$791$	−10.4133	−	18.0364i	−0.370255	−	0.641301i
$792$		0			0
$793$	13.5818	−	23.5243i	0.482303	−	0.835374i
$794$		0			0
$795$	−71.7609	−	37.5271i	−2.54510	−	1.33095i
$796$		0			0
$797$	4.95293	−	1.80272i	0.175442	−	0.0638556i	−0.252806	−	0.967517i	$-0.581353\pi$
$797$	4.95293	−	1.80272i	0.175442	−	0.0638556i	0.428248	+	0.903661i	$0.359131\pi$
$798$		0			0
$799$	0.204950	+	1.16233i	0.00725060	+	0.0411202i
$800$		0			0
$801$	2.88270	−	31.5884i	0.101855	−	1.11612i
$802$		0			0
$803$	31.6098	−	26.5237i	1.11548	−	0.936002i
$804$		0			0
$805$	−11.1071	+	62.9916i	−0.391475	+	2.22016i
$806$		0			0
$807$	12.8442	−	40.4727i	0.452139	−	1.42471i
$808$		0			0
$809$	−34.9291			−1.22804			−0.614021	−	0.789290i	$-0.710449\pi$
$809$	−34.9291			−1.22804			−0.614021	+	0.789290i	$0.710449\pi$
$810$		0			0
$811$	−43.5746			−1.53011			−0.765056	−	0.643963i	$-0.777289\pi$
$811$	−43.5746			−1.53011			−0.765056	+	0.643963i	$0.777289\pi$
$812$		0			0
$813$	−7.67702	+	24.1906i	−0.269245	+	0.848401i
$814$		0			0
$815$	10.2902	−	58.3585i	0.360449	−	2.04421i
$816$		0			0
$817$	6.50047	−	5.45454i	0.227423	−	0.190830i
$818$		0			0
$819$	−17.8577	+	8.24602i	−0.623999	+	0.288139i
$820$		0			0
$821$	4.64298	+	26.3317i	0.162041	+	0.918981i	0.952063	+	0.305902i	$0.0989581\pi$
$821$	4.64298	+	26.3317i	0.162041	+	0.918981i	−0.790022	+	0.613079i	$0.789931\pi$
$822$		0			0
$823$	14.4592	−	5.26272i	0.504016	−	0.183447i	−0.0774835	−	0.996994i	$-0.524688\pi$
$823$	14.4592	−	5.26272i	0.504016	−	0.183447i	0.581499	+	0.813547i	$0.302466\pi$
$824$		0			0
$825$	57.9755	+	30.3181i	2.01845	+	1.05554i
$826$		0			0
$827$	8.18203	−	14.1717i	0.284517	−	0.492798i	−0.687975	−	0.725735i	$-0.741500\pi$
$827$	8.18203	−	14.1717i	0.284517	−	0.492798i	0.972492	+	0.232936i	$0.0748334\pi$
$828$		0			0
$829$	−0.0462659	−	0.0801348i	−0.00160688	−	0.00278320i	0.865221	−	0.501391i	$-0.167178\pi$
$829$	−0.0462659	−	0.0801348i	−0.00160688	−	0.00278320i	−0.866828	+	0.498608i	$0.833845\pi$
$830$		0			0
$831$	8.67326	+	21.0503i	0.300872	+	0.730228i
$832$		0			0
$833$	−0.414395	−	0.347719i	−0.0143579	−	0.0120477i
$834$		0			0
$835$	25.7673	+	9.37852i	0.891714	+	0.324557i
$836$		0			0
$837$	−22.2737	−	1.09770i	−0.769891	−	0.0379422i
$838$		0			0
$839$	3.59914	+	1.30998i	0.124256	+	0.0452255i	0.403400	−	0.915024i	$-0.367828\pi$
$839$	3.59914	+	1.30998i	0.124256	+	0.0452255i	−0.279144	+	0.960249i	$0.590051\pi$
$840$		0			0
$841$	45.0571	+	37.8074i	1.55369	+	1.30370i
$842$		0			0
$843$	46.6509	+	6.23047i	1.60674	+	0.214589i
$844$		0			0
$845$	−6.00876	−	10.4075i	−0.206708	−	0.358028i
$846$		0			0
$847$	7.03662	−	12.1878i	0.241781	−	0.418777i
$848$		0			0
$849$	1.04738	+	25.0644i	0.0359461	+	0.860207i
$850$		0			0
$851$	−45.0796	+	16.4076i	−1.54531	+	0.562447i
$852$		0			0
$853$	−2.54185	−	14.4156i	−0.0870314	−	0.493579i	−0.996900	−	0.0786824i	$-0.974929\pi$
$853$	−2.54185	−	14.4156i	−0.0870314	−	0.493579i	0.909868	−	0.414897i	$-0.136182\pi$
$854$		0			0
$855$	−23.8319	−	6.48135i	−0.815033	−	0.221657i
$856$		0			0
$857$	−5.33556	+	4.47707i	−0.182259	+	0.152934i	−0.729353	−	0.684138i	$-0.760179\pi$
$857$	−5.33556	+	4.47707i	−0.182259	+	0.152934i	0.547093	+	0.837072i	$0.315734\pi$
$858$		0			0
$859$	6.68715	−	37.9247i	0.228163	−	1.29397i	−0.628383	−	0.777904i	$-0.716283\pi$
$859$	6.68715	−	37.9247i	0.228163	−	1.29397i	0.856546	−	0.516071i	$-0.172606\pi$
$860$		0			0
$861$	20.6815	+	22.6548i	0.704825	+	0.772075i
$862$		0			0
$863$	−5.26893			−0.179356			−0.0896782	−	0.995971i	$-0.528584\pi$
$863$	−5.26893			−0.179356			−0.0896782	+	0.995971i	$0.528584\pi$
$864$		0			0
$865$	33.3176			1.13283
$866$		0			0
$867$	28.6859	−	6.30327i	0.974225	−	0.214070i
$868$		0			0
$869$	1.92501	−	10.9173i	0.0653014	−	0.370343i
$870$		0			0
$871$	2.61885	−	2.19748i	0.0887363	−	0.0744586i
$872$		0			0
$873$	−3.17319	+	6.73901i	−0.107396	+	0.228081i
$874$		0			0
$875$	5.40784	+	30.6694i	0.182818	+	1.03682i
$876$		0			0
$877$	−10.5084	+	3.82475i	−0.354844	+	0.129153i	−0.513290	−	0.858215i	$-0.671574\pi$
$877$	−10.5084	+	3.82475i	−0.354844	+	0.129153i	0.158447	+	0.987368i	$0.449351\pi$
$878$		0			0
$879$	3.39439	−	2.15355i	0.114490	−	0.0726376i
$880$		0			0
$881$	0.532342	−	0.922044i	0.0179351	−	0.0310645i	−0.856919	−	0.515452i	$-0.827624\pi$
$881$	0.532342	−	0.922044i	0.0179351	−	0.0310645i	0.874854	+	0.484387i	$0.160957\pi$
$882$		0			0
$883$	5.23279	+	9.06346i	0.176097	+	0.305010i	0.940541	−	0.339681i	$-0.110319\pi$
$883$	5.23279	+	9.06346i	0.176097	+	0.305010i	−0.764443	+	0.644691i	$0.776986\pi$
$884$		0			0
$885$	−39.1723	+	50.8532i	−1.31676	+	1.70941i
$886$		0			0
$887$	25.3875	+	21.3027i	0.852429	+	0.715273i	0.960323	−	0.278889i	$-0.0899662\pi$
$887$	25.3875	+	21.3027i	0.852429	+	0.715273i	−0.107894	+	0.994162i	$0.534411\pi$
$888$		0			0
$889$	−9.61348	−	3.49902i	−0.322426	−	0.117353i
$890$		0			0
$891$	32.9454	−	18.6939i	1.10371	−	0.626270i
$892$		0			0
$893$	−11.7700	−	4.28394i	−0.393869	−	0.143356i
$894$		0			0
$895$	72.5089	+	60.8422i	2.42371	+	2.03373i
$896$		0			0
$897$	26.9913	−	35.0398i	0.901212	−	1.16995i
$898$		0			0
$899$	−20.1094	−	34.8304i	−0.670685	−	1.16166i
$900$		0			0
$901$	1.29769	−	2.24766i	0.0432322	−	0.0748803i
$902$		0			0
$903$	−11.8120	+	7.49407i	−0.393079	+	0.249387i
$904$		0			0
$905$	−28.1970	+	10.2629i	−0.937298	+	0.341149i
$906$		0			0
$907$	−1.64061	−	9.30438i	−0.0544757	−	0.308947i	0.945379	−	0.325972i	$-0.105692\pi$
$907$	−1.64061	−	9.30438i	−0.0544757	−	0.308947i	−0.999855	+	0.0170252i	$0.994580\pi$
$908$		0			0
$909$	3.70380	−	0.310088i	0.122847	−	0.0102850i
$910$		0			0
$911$	−28.5977	+	23.9963i	−0.947483	+	0.795033i	−0.978872	−	0.204474i	$-0.934452\pi$
$911$	−28.5977	+	23.9963i	−0.947483	+	0.795033i	0.0313886	+	0.999507i	$0.490007\pi$
$912$		0			0
$913$	−5.18977	+	29.4327i	−0.171756	+	0.974079i
$914$		0			0
$915$	−54.9151	+	12.0667i	−1.81544	+	0.398913i
$916$		0			0
$917$	42.3531			1.39862
$918$		0			0
$919$	15.1980			0.501336			0.250668	−	0.968073i	$-0.419350\pi$
$919$	15.1980			0.501336			0.250668	+	0.968073i	$0.419350\pi$
$920$		0			0
$921$	30.8937	+	33.8414i	1.01798	+	1.11511i
$922$		0			0
$923$	2.53479	−	14.3755i	0.0834336	−	0.473175i
$924$		0			0
$925$	−40.4009	+	33.9004i	−1.32837	+	1.11464i
$926$		0			0
$927$	−33.7004	+	33.4493i	−1.10687	+	1.09862i
$928$		0			0
$929$	−4.78628	−	27.1443i	−0.157033	−	0.890577i	−0.956904	−	0.290405i	$-0.906210\pi$
$929$	−4.78628	−	27.1443i	−0.157033	−	0.890577i	0.799871	−	0.600172i	$-0.204901\pi$
$930$		0			0
$931$	5.39462	−	1.96348i	0.176802	−	0.0643505i
$932$		0			0
$933$	−2.43947	−	58.3777i	−0.0798647	−	1.91120i
$934$		0			0
$935$	−1.63249	+	2.82755i	−0.0533881	+	0.0924708i
$936$		0			0
$937$	−6.39233	−	11.0718i	−0.208828	−	0.361701i	0.742517	−	0.669827i	$-0.233632\pi$
$937$	−6.39233	−	11.0718i	−0.208828	−	0.361701i	−0.951346	+	0.308126i	$0.900298\pi$
$938$		0			0
$939$	8.21592	+	1.09728i	0.268116	+	0.0358083i
$940$		0			0
$941$	40.6491	+	34.1087i	1.32512	+	1.11191i	0.985191	+	0.171461i	$0.0548487\pi$
$941$	40.6491	+	34.1087i	1.32512	+	1.11191i	0.339933	+	0.940450i	$0.389596\pi$
$942$		0			0
$943$	−64.8181	−	23.5919i	−2.11077	−	0.768257i
$944$		0			0
$945$	37.5266	+	15.7912i	1.22074	+	0.513688i
$946$		0			0
$947$	−14.6267	−	5.32368i	−0.475303	−	0.172996i	0.0932499	−	0.995643i	$-0.470274\pi$
$947$	−14.6267	−	5.32368i	−0.475303	−	0.172996i	−0.568553	+	0.822646i	$0.692497\pi$
$948$		0			0
$949$	−23.4933	−	19.7132i	−0.762626	−	0.639919i
$950$		0			0
$951$	14.3287	+	34.7763i	0.464640	+	1.12770i
$952$		0			0
$953$	17.1470	+	29.6995i	0.555445	+	0.962060i	0.997869	+	0.0652533i	$0.0207855\pi$
$953$	17.1470	+	29.6995i	0.555445	+	0.962060i	−0.442423	+	0.896806i	$0.645881\pi$
$954$		0			0
$955$	21.5458	−	37.3184i	0.697205	−	1.20759i
$956$		0			0
$957$	60.5369	+	31.6575i	1.95688	+	1.02334i
$958$		0			0
$959$	4.23626	−	1.54187i	0.136796	−	0.0497896i
$960$		0			0
$961$	−2.18461	−	12.3895i	−0.0704713	−	0.399662i
$962$		0			0
$963$	7.70461	+	5.43788i	0.248278	+	0.175233i
$964$		0			0
$965$	69.9377	−	58.6847i	2.25137	−	1.88913i
$966$		0			0
$967$	−1.55514	+	8.81962i	−0.0500098	+	0.283620i	−0.999549	−	0.0300285i	$-0.990440\pi$
$967$	−1.55514	+	8.81962i	−0.0500098	+	0.283620i	0.949539	+	0.313648i	$0.101551\pi$
$968$		0			0
$969$	0.239430	−	0.754452i	0.00769159	−	0.0242365i
$970$		0			0
$971$	−27.7605			−0.890875			−0.445438	−	0.895313i	$-0.646952\pi$
$971$	−27.7605			−0.890875			−0.445438	+	0.895313i	$0.646952\pi$
$972$		0			0
$973$	−8.21581			−0.263387
$974$		0			0
$975$	14.7086	−	46.3474i	0.471053	−	1.48431i
$976$		0			0
$977$	6.50414	−	36.8868i	0.208086	−	1.18011i	−0.684423	−	0.729085i	$-0.739946\pi$
$977$	6.50414	−	36.8868i	0.208086	−	1.18011i	0.892509	−	0.451029i	$-0.148943\pi$
$978$		0			0
$979$	34.0898	−	28.6047i	1.08951	−	0.914210i
$980$		0			0
$981$	−36.4767	−	25.7451i	−1.16461	−	0.821977i
$982$		0			0
$983$	4.43397	+	25.1463i	0.141422	+	0.802042i	0.970171	+	0.242422i	$0.0779418\pi$
$983$	4.43397	+	25.1463i	0.141422	+	0.802042i	−0.828749	+	0.559620i	$0.810947\pi$
$984$		0			0
$985$	−2.10101	+	0.764705i	−0.0669437	+	0.0243655i
$986$		0			0
$987$	18.2972	+	9.56844i	0.582406	+	0.304567i
$988$		0			0
$989$	15.7279	−	27.2416i	0.500120	−	0.866233i
$990$		0			0
$991$	2.78119	+	4.81717i	0.0883475	+	0.153022i	0.906813	−	0.421534i	$-0.138508\pi$
$991$	2.78119	+	4.81717i	0.0883475	+	0.153022i	−0.818465	+	0.574556i	$0.805175\pi$
$992$		0			0
$993$	−17.5398	−	42.5698i	−0.556610	−	1.35091i
$994$		0			0
$995$	23.9980	+	20.1367i	0.760787	+	0.638376i
$996$		0			0
$997$	19.8990	+	7.24265i	0.630208	+	0.229377i	0.637322	−	0.770598i	$-0.280042\pi$
$997$	19.8990	+	7.24265i	0.630208	+	0.229377i	−0.00711392	+	0.999975i	$0.502264\pi$
$998$		0			0
$999$	3.81579	+	30.2960i	0.120726	+	0.958524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.c.193.6	yes	54
4.3	odd	2		864.2.y.b.193.4	✓	54
27.7	even	9	inner	864.2.y.c.385.6	yes	54
108.7	odd	18		864.2.y.b.385.4	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.4	✓	54	4.3	odd	2
864.2.y.b.385.4	yes	54	108.7	odd	18
864.2.y.c.193.6	yes	54	1.1	even	1	trivial
864.2.y.c.385.6	yes	54	27.7	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.523926 - 1.65091i) q^{3} +(-0.649143 + 3.68147i) q^{5} +(-1.60562 + 1.34727i) q^{7} +(-2.45100 - 1.72991i) q^{9} +O(q^{10})\)	\(q+(0.523926 - 1.65091i) q^{3} +(-0.649143 + 3.68147i) q^{5} +(-1.60562 + 1.34727i) q^{7} +(-2.45100 - 1.72991i) q^{9} +(-0.730858 - 4.14490i) q^{11} +(-2.93949 + 1.06989i) q^{13} +(5.73767 + 3.00049i) q^{15} +(-0.103757 + 0.179712i) q^{17} +(-1.10111 - 1.90718i) q^{19} +(1.38300 + 3.35660i) q^{21} +(-6.25355 - 5.24735i) q^{23} +(-8.43338 - 3.06950i) q^{25} +(-4.14006 + 3.14004i) q^{27} +(-8.80597 - 3.20511i) q^{29} +(3.28769 + 2.75870i) q^{31} +(-7.22577 - 0.965040i) q^{33} +(-3.91768 - 6.78562i) q^{35} +(2.93827 - 5.08923i) q^{37} +(0.226213 + 5.41337i) q^{39} +(7.94006 - 2.88995i) q^{41} +(0.669113 + 3.79473i) q^{43} +(7.95965 - 7.90034i) q^{45} +(4.35696 - 3.65593i) q^{47} +(-0.452672 + 2.56723i) q^{49} +(0.242328 + 0.265449i) q^{51} -12.5070 q^{53} +15.7338 q^{55} +(-3.72549 + 0.818615i) q^{57} +(-1.72153 + 9.76330i) q^{59} +(-6.65204 + 5.58172i) q^{61} +(6.26604 - 0.524603i) q^{63} +(-2.03061 - 11.5162i) q^{65} +(-1.02697 + 0.373785i) q^{67} +(-11.9393 + 7.57483i) q^{69} +(-2.33322 + 4.04125i) q^{71} +(4.90201 + 8.49053i) q^{73} +(-9.48593 + 12.3146i) q^{75} +(6.75780 + 5.67047i) q^{77} +(2.47506 + 0.900847i) q^{79} +(3.01484 + 8.48002i) q^{81} +(-6.67269 - 2.42866i) q^{83} +(-0.594253 - 0.498637i) q^{85} +(-9.90502 + 12.8586i) q^{87} +(5.28661 + 9.15667i) q^{89} +(3.27827 - 5.67813i) q^{91} +(6.27687 - 3.98233i) q^{93} +(7.73601 - 2.81568i) q^{95} +(-0.431152 - 2.44518i) q^{97} +(-5.37896 + 11.4235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q + 9 q^{11} + 12 q^{17} - 18 q^{19} + 12 q^{21} + 21 q^{27} + 6 q^{29} - 36 q^{31} - 9 q^{33} - 24 q^{39} + 3 q^{41} + 21 q^{43} + 42 q^{45} - 18 q^{49} - 24 q^{51} + 36 q^{53} + 72 q^{55} + 39 q^{57} - 18 q^{59} - 18 q^{61} + 30 q^{63} + 48 q^{65} + 27 q^{67} + 24 q^{69} + 84 q^{75} + 36 q^{77} - 72 q^{79} + 36 q^{81} - 6 q^{87} + 33 q^{89} - 36 q^{91} + 72 q^{93} - 36 q^{95} + 9 q^{97} - 120 q^{99}+O(q^{100}) \) 54 * q + 9 * q^11 + 12 * q^17 - 18 * q^19 + 12 * q^21 + 21 * q^27 + 6 * q^29 - 36 * q^31 - 9 * q^33 - 24 * q^39 + 3 * q^41 + 21 * q^43 + 42 * q^45 - 18 * q^49 - 24 * q^51 + 36 * q^53 + 72 * q^55 + 39 * q^57 - 18 * q^59 - 18 * q^61 + 30 * q^63 + 48 * q^65 + 27 * q^67 + 24 * q^69 + 84 * q^75 + 36 * q^77 - 72 * q^79 + 36 * q^81 - 6 * q^87 + 33 * q^89 - 36 * q^91 + 72 * q^93 - 36 * q^95 + 9 * q^97 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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